Inequality and Panel Income Changes: Conditions for Possibilities and Impossibilities

The question of who benefits from economic growth is most commonly assessed by using anonymous data from comparable cross sections to calculate changes in income inequality. An alternative is to utilize longitudinal data and assess the pattern of panel income changes. In this paper, we derive precise theoretical conditions reconciling various measures of rising/falling inequality together with various measures of convergent/divergent panel income changes. We have four main findings: i) for a large number of inequality indices, as well as for Lorenz curves, we derive precise conditions for rising inequality and convergent panel income changes to coexist, ii) we demonstrate that in order to observe both rising inequality and panel convergence, income changes in the panel have to be ``large'' (and in the right direction), where the meaning of ``large'' varies depending on the particular regression under analysis, iii) for a large number of inequality indices, as well as for Lorenz curves, we show that it is impossible to have both falling inequality together with divergent panel income changes in shares or in proportions, iv) we find a precise relationship between convergence/divergence of panel income changes in dollars on the one hand and the coefficient of variation, the correlation coefficient be- tween initial and final incomes, and the aggregate economic growth rate on the other.